Acoustic Waves in the Universe as a Powerful

Cosmological Probe

Eiichiro KomatsuDepartment of Astronomy, UT

Acoustic Seminar, March 2, 2007

Our Universe Is Old

The latest determination of the age of our Universe is: 13.730.16 billion years

How was it determined? In essence, (time) = (distance)/c was used. “Distance” to what??

It must be a distance to the farthest place we could reach. The Rule: “Farthest Place” = “Earliest Epoch”

For the errorbar to make sense, obviously it must be earlier than 160 million years after the Big Bang.

So, what is the earliest epoch that we can see directly?

The Most Distant Galaxy?

Going Farther…

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How far have we reached?

Our Universe is 13.73 billion years old.

The most distant galaxy currently known is seen at 800 million years after the Big Bang. 1/17 of the age of t

he Universe today

How far can we reach? Galaxies cannot be used to determine the age

of the Universe accurately. Distant galaxies are very faint and difficult to find.

Fundamental “flaw” in this method: galaxies cannot be as old as the Universe itself --- after all, it takes some time (~hundreds of millions of years) to form galaxies.

So, is 800 million years after the Big Bang the farthest place we can ever reach?NO!

Night Sky in Optical (~0.5nm)

Night Sky in Microwave (~1mm)

Full Sky Microwave Map

Penzias & Wilson, 1965Uniform, “Fossil” Light from the Big Bang

-Isotropic (2.7 K everywhere)

-Unpolarized

Galactic CenterGalactic Anti-center

A. Penzias & R. Wilson, 1965

CMBT = 2.73 K

Helium SuperfluidityT = 2.17 K

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COBE/DMR, 1992

Isotropic?

CMB is anisotropic! (at the 1/100,000 level)

COBE to WMAPCOBE

WMAP

COBE1989

WMAP2001

[COBE’s] measurements also marked the inception of cosmology as a precise science. It was not long before it was followed up, for instance by the WMAP satellite, which yielded even clearer images of the background radiation.

Press Release from the Nobel Foundation

CMB: The Most Distant Light

CMB was emitted when the Universe was only 380,000 years old. WMAP has measured the distance to this epoch. From (time)=(distance)/c we obtained 13.73 0.16 billion years.

Use Ripples in CMB to Measure Composition of the Universe

The Basic Idea: Hit it and listen to the cosmic sound. Analogy: Brass and ceramic can be discriminated by hitting them and li

stening to the sound created by them. We can use sound waves to determine composition.

When CMB was emitted the Universe was a dense and hot soup of photons, electrons, protons, Helium nuclei, and dark matter particles. Ripples in CMB propagate in the cosmic soup: the pattern of the ripple

s, the cosmic sound wave, can be used to determine composition of the Universe!

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Composition of Our Universe Determined by WMAP

Dark Energy

Ordinary Matter

Dark Matter

76%

20%

4%

Mysterious “Dark Energy” occupies 75.93.4% of the total energy of the Universe.

How do we “hear” the cosmic sound from this?

Do the Fourier Analysis: The Angular Power Spectrum

CMB temperature anisotropy is very close to Gaussian; thus, its spherical harmonic transform, alm, is also Gaussian.

Since alm is Gaussian, the power spectrum:

completely specifies statistical properties of CMB.

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Cl = almalm*

Cosmic Sound Wave!

What the Sound Wave Tells Us

Distance to z~1100

Baryon-to-Photon Ratio

Matter-Radiation Equality Epoch

Dark Energy/New Physics?

R. Sachs and A. Wolfe, 1967

•SOLVE GENERAL RELATIVISTIC BOLTZMANN SOLVE GENERAL RELATIVISTIC BOLTZMANN EQUATIONS TO THE FIRST ORDER IN PERTURBATIONSEQUATIONS TO THE FIRST ORDER IN PERTURBATIONS

Introduce temperature fluctuations, =T/T:

Expand the Boltzmann equation to the first order:

where

describes the Sachs-Wolfe effect: purely GR-induced fluctuations.

For metric perturbations in the form of:

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ds2 = a2 −1+ h00( )dτ 2 + δ ij + hij( )dx idx j[ ]

the Sachs-Wolfe terms are given by

where is the directional cosine of photon propagations.

Newtonian potential Curvature perturbations

1. The 1st term = gravitational redshift

2. The 2nd term = integrated Sachs-Wolfe effect

h00/2

hij/2

(higher T)

Sound Waves From Hydrodynamical Perturbations

When coupling is strong, photons and baryons move together and behave as a single, perfect fluid.

When coupling becomes less strong, they behave as an imperfect fluid with viscosity.

So, the problem can be formulated as “hydrodynamics”. (cf S-W effect was pure GR.)

Collision term describing coupling between photons and baryons via electron scattering.

Boltzmann to Hydrodynamics

Multipole expansion

Energy density, Velocity, StressEnergy density

Velocity

Stress

Photons

f2=9/10 (no polarization), 3/4 (with polarization)

A = -h00/2, H = hii/2

C=Thomson scattering optical depth

CONTINUITY

EULER

Photon-baryon coupling

Baryons

Cold Dark Matter

Approximate Equation System in the Strong Coupling Regime

SOUND WAVE!

A Big, Big Challenge

Let’s face it: “WMAP has done a great job in determining composition of our Universe very accurately, but…” We don’t really understand the nature of dark energy

or dark matter. They occupy 96% of the total energy in our Universe!

Even the most optimistic cosmologists would not dare to say, “we understand our Universe”. Definitely not.

The next frontier: What is the nature of dark energy and dark matter?

A Holy Grail: Go Even Farther Back…

We cannot use CMB to probe the epoch earlier than 380,000 years after the Big Bang directly. Photons were scattered by electrons so frequently tha

t the Universe was literally “foggy” to photons. We would need to stop relying on photons (EM

waves). What else? Neutrinos can probe the epoch as early as a second a

fter the Big Bang. Gravity Waves: the ultimate probe of the earliest mom

ent of the Universe.

Go Farther!

CMB

Neutrino

Gravity Wave

Summary & Conclusions CMB offers the earliest and most precise picture of the Universe th

at we have today. A wealth of cosmological information, e.g.

The age of the Universe = 13.73 billion years Composition: DE (76%), DM (20%), Ordinary Mat. (4%)

CMB has limitations. It does not tell us much about the nature of the most dominant energy comp

onents in the Universe: Dark Energy (DE) and Dark Matter (DM) Expect some news on DM from the Large Hadron Collider (LHC) next year. DE is harder to do.

Go beyond CMB. Neutrinos! (Very low energy: 1.94K -> hard to detect) Gravity waves! The ultimate cosmological probe.